Getting on a plane

2017 passengers are boarding a plane that seats 2017 people. Each passenger has an assigned seat. However, the first three passengers do not sit in their assigned seats, and instead sit in a random empty seat. After that, each subsequent passenger sits on their assigned seat, unless it is already occupied, in which case they also sit on a random empty seat. What is the probability that the last passenger to board the plane sits on his assigned seat?

If you think the answer is \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, input your answer as \(a+b\).

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.